THE STRAIGHT LINE LAW 447 



presents the quantity plotted horizontally, and y the quantity 

 plotted vertically. For greater generality the straight line law 

 could be stated as 



V - mH. + c 



where V is the quantity plotted vertically, and II the quantity 

 plotted horizontally. It does not matter in what way the quantities 

 V and H have been derived, or what form they take, but if the 

 above relation connects them, and m and c are constants, then a 

 straight line must be the result of plotting V vertically and H 

 horizontally. Thus, for example, if a set of tabular values of 

 x and y is given, the quantity V can be derived in some way from 

 the values of both x and y, and this also can be the case for the 

 quantity H ; there can be a straight line law connecting V and H, 

 although there need not necessarily be a straight line law connect- 

 ing y and x. 



216. The Determination of the Constants. If a straight line has 

 been obtained by plotting some quantity V vertically and another 

 quantity H horizontally, this line can be expressed in the form of 

 an algebraic law connecting V and H if the numerical values of the 

 constants m and c are found. The values of the constants can 

 be found in two different waj's. 



(a) It has already been shown that m represents the slope of 

 the line and c is the distance, above or below the origin, of the 

 point of intersection of the line and the axis of y. Thus the values 

 of these constants can be found from these statements. If the 

 origin is accessible the point of intersection of the line and the axis 

 of y can be found and the value of c can be read off along the axis 

 of y. The slope m can be measured in the usual way. Take two 

 points A and B on the line, make AB the hypotenuse of a right 

 angled triangle, the base of which is parallel to the axis of x. Let 

 the perpendicular of this triangle be measured by means of the 

 vertical scale and the base measured by means of the horizontal 

 scale, 



perpendicular 



then m = . 



base 



Generally speaking, this is not the best way of determining the 

 values of the constants, because in actual practice it need not 

 be necessary, except in a very few cases, to work from the origin, 

 and if the origin is inaccessible the value of the constant c cannot 

 be found directly. Then the constants can be found by solving 

 a pair of simultaneous equations, and this gives rise to the second 

 way. 



(b) Take two points on the line as far removed as the range of 

 values permits ; it is unwise to work outside this range. If 



